Answer:
Step-by-step explanation:
You need the Pythagorean Theorem to solve this question. There is no be part.
Equation
c^2 = a^2 + b^2
Givens
a = 32
b = 21
c = ?
Solution
c^2 = a^2 + b^2 Substitute the values
c^2 = 32^2 + 21^2 Expand
c^2 = 1024 + 441 Combine
c^2 = 1465 Take the square root of both sides
√c^2 = √1465
c = 38.275
Answer: 38.3 rounded
Answer:
The width and length of rectangle is 12.728 m
Step-by-step explanation:
Let the length of the rectangle = L
let the width of the rectangle = W
The subjective function is given by;
F(p) = 2(L + W)
F = 2L + 2W
Area of the rectangle is given by;
A = LW
LW = 162 ft²
L = 162 / W
Substitute in the value of L into subjective function;
![f = 2l + 2w\\\\f = 2(\frac{162}{w} )+2w\\\\f = \frac{324}{w} + 2w\\\\\frac{df}{dw} = \frac{-324}{w^2} +2\\\\](https://tex.z-dn.net/?f=f%20%3D%202l%20%2B%202w%5C%5C%5C%5Cf%20%3D%202%28%5Cfrac%7B162%7D%7Bw%7D%20%29%2B2w%5C%5C%5C%5Cf%20%3D%20%5Cfrac%7B324%7D%7Bw%7D%20%2B%202w%5C%5C%5C%5C%5Cfrac%7Bdf%7D%7Bdw%7D%20%3D%20%5Cfrac%7B-324%7D%7Bw%5E2%7D%20%2B2%5C%5C%5C%5C)
Take the second derivative of the function, to check if it will given a minimum perimeter
![\frac{d^2f}{dw^2}= \frac{648}{w^3} \\\\Thus, \frac{d^2f}{dw^2}>0, \ since,\frac{648}{w^3} >0 \ (minimum \ function \ verified)](https://tex.z-dn.net/?f=%5Cfrac%7Bd%5E2f%7D%7Bdw%5E2%7D%3D%20%5Cfrac%7B648%7D%7Bw%5E3%7D%20%5C%5C%5C%5CThus%2C%20%5Cfrac%7Bd%5E2f%7D%7Bdw%5E2%7D%3E0%2C%20%5C%20since%2C%5Cfrac%7B648%7D%7Bw%5E3%7D%20%3E0%20%5C%20%28minimum%20%5C%20function%20%5C%20verified%29)
Determine the critical points of the first derivative;
df/dw = 0
![\frac{-324}{w^2} +2 = 0\\\\-324 + 2w^2=0\\\\2w^2 = 324\\\\w^2 = \frac{324}{2} \\\\w^2 = 162\\\\w= \sqrt{162}\\\\w = 12.728 \ m](https://tex.z-dn.net/?f=%5Cfrac%7B-324%7D%7Bw%5E2%7D%20%2B2%20%3D%200%5C%5C%5C%5C-324%20%2B%202w%5E2%3D0%5C%5C%5C%5C2w%5E2%20%3D%20324%5C%5C%5C%5Cw%5E2%20%3D%20%5Cfrac%7B324%7D%7B2%7D%20%5C%5C%5C%5Cw%5E2%20%3D%20162%5C%5C%5C%5Cw%3D%20%5Csqrt%7B162%7D%5C%5C%5C%5Cw%20%3D%2012.728%20%5C%20m)
L = 162 / 12.728
L = 12.728 m
Therefore, the width and length of rectangle is 12.728 m
The mode is the number that repeats itself the most in a sequence. In this case, the mode will be £140 since it repeats itslef the most (2 times).
Hope it helped,
BioTeacher101